Bioinspiration & Biomimetics

Robotic herding offers a promising off-animal approach to controlling the spatial distribution of grazing livestock. Nevertheless, the habituation of cattle to herding stimuli remains a critical obstacle to its practical use. This study presents the first field investigation of behavioral responses of grazing cattle to herding by a quadruped robot. We compared the herding efficacy of a drone and a quadruped robot, and tracked daily changes in responsiveness during continuous herding. Trials were conducted in a 1.1-ha pasture with Japanese Black breeding cows from June to October 2023. The quadruped robot elicited stronger avoidance responses with shorter latencies than the drone, and herding was more successful with the robot. During consecutive daily herding with the robot, behavioral responsiveness declined progressively over the initial 5 days, at a markedly slower rate than previously reported for drone herding. Following a 24-day interruption, responsiveness partially increased, but declined rapidly again over the subsequent two days. These results indicate that the quadruped robot constitutes a more persistent aversive stimulus than a drone for grazing cattle, although habituation management strategies (such as diversifying stimuli or combining sensory modalities) will be necessary for sustained control of grazing distribution.

The queen bee is the central individual responsible for colony establishment, growth, and survival. Reliable confirmation of successful mating, continued queen presence, and normal reproductive performance is essential for effective colony management. We present a queen bee detection system based on an array of Hall-effect sensors and a miniature magnetic tag attached to the queen. The system is designed for continuous operation and real-time monitoring. A prototype was developed, constructed, and evaluated under both laboratory and field conditions. Field experiments conducted in an apiary demonstrated that the system can reliably detect queen bee passages through the hive entrance, enabling the identification of activities associated with mating flights. The results confirm the feasibility of Hall-effect sensing for automated, non-invasive queen bee monitoring and establish magnetic sensing as a promising new measurement modality for precision apiculture.

Background and AimsActive capsule endoscopy could advance gastrointestinal diagnostics by enabling controlled navigation beyond passive peristalsis. However, current systems are often limited by inefficient propulsion, high power demands, or reliance on external actuation. Herein, we designed, developed and evaluated a novel electromagnetic impact-actuated capsule endoscope incorporating a ferromagnetic rail-enhanced locomotion mechanism. MethodsThe capsule employed an internal electromagnetic actuator comprising a movable coil-armature assembly guided along a ferromagnetic rail and surrounded by permanent magnets. Controlled current pulses generated reciprocating motion and propulsion through momentum transfer. Bench-top testing using a deformable intestinal model assessed locomotion and power consumption. Ex-vivo experiments were subsequently performed in porcine intestine under dry and physiologically simulated wet conditions. Transit speed, power consumption, and system stability were recorded. ResultsBench-top testing demonstrated stable propulsion at speeds up to 8.5 mm/s with a mean power consumption of 84 mW. During ex-vivo evaluation, mean capsule velocities were 1.95 mm/s and 7.2 mm/s under dry and wet conditions, respectively. Average power consumption was 96 mW and 193 mW. The actuator maintained reliable locomotion while preserving a compact system volume of [~]6.19 cm3. Lubricated conditions, representative of the intestinal environment, resulted in enhanced propulsion efficiency despite a concomitant increase in instantaneous power consumption. ConclusionThe electromagnetic impact-actuated capsule demonstrated reliable locomotion in biologically relevant ex-vivo environments while maintaining compact dimensions and moderate power requirements. Ferromagnetic rail-enhanced flux concentration offers a promising propulsion strategy for future actively navigated and therapeutic capsule endoscopy platforms.

Collective motion emerges from local interactions among individuals, yet whether interaction rules inferred from trajectory data correspond to the mechanisms actually used by animals remains unresolved. Here, we address this question using an autonomous closed-loop robotic fish implementing a data-driven model of social interactions reconstructed from the schooling fish Hemigrammus rhodostomus. The robot continuously updated its behavior from real-time tracking of freely swimming fish while reproducing spontaneous locomotion, wall avoidance, and anisotropic attraction and alignment. We compared entirely biological groups, biohybrid groups containing one robotic fish, and numerical simulations using identical behavioral descriptors across isolated individuals, pairs, and groups of five fish. The robotic fish successfully integrated into natural schools and reproduced the principal signatures of collective coordination, providing the first direct causal validation of interaction rules reconstructed from behavioral trajectories. Biohybrid experiments showed that a robot responding only to its single most influential neighbor was sufficient to sustain natural collective coordination. By contrast, numerical simulations reproduced the behavior of biological groups most accurately when each fish interacted with its two most influential neighbors. This discrepancy identifies the contribution of hydrodynamic interactions, which remain available to living fish but are absent from the robotic controller, demonstrating that physical and behavioral interactions jointly shape collective organization. These findings establish closed-loop biohybrid robotics as a powerful framework for experimentally testing the mechanisms underlying collective animal behavior. SignificanceInferring the behavioral mechanisms underlying collective animal behavior from trajectory data alone cannot establish causality. We combined a data-driven model of fish social interactions with an autonomous closed-loop robotic fish that continuously interacted with freely swimming conspecifics. This biohybrid approach provides the first direct causal validation of interaction rules reconstructed from behavioral trajectories. Comparing biological groups, biohybrid groups, and numerical simulations further reveals that hydrodynamic interactions complement social interactions in shaping collective organization. While living fish require information from their two most influential neighbors to reproduce natural schools, a robotic fish lacking hydrodynamic feedback achieves comparable coordination by responding to only its single most influential neighbor, demonstrating the power of closed-loop biohybrid robotics for testing mechanisms of collective behavior.

Advances in camera technology and computer vision techniques have allowed researchers to track animals in 3D in ways which previously were difficult or impossible. Many such 3D tracking tools make use of multiple cameras, but unfamiliarity with the principles and technology involved can make it difficult to employ such techniques. In this protocol, we describe Braid, open-source software for live, multi-camera 3D tracking of insects. Using background-subtraction, Braid performs detection of objects without requiring the use of physical markers affixed to the insect. Braid constructs low-latency 3D position estimates using Kalman filtering and nearest neighbor data association. We document in detail the process of tracking freely flying bees within a flight arena using Braid. This protocol includes instructions on installation, configuration of cameras, setup, calibration, and operation. Within the system described here, we demonstrate that Braid can achieve position estimates accurate to <1 millimeter (within a 0.3 cubic meter volume). These factors make Braid suitable for tracking small, fast-flying animals like insects. Braid's low latency allows live tracking, removing the necessity to collect large video files and making it suitable for integration in closed loop systems such as virtual reality. Code is available at https://github.com/strawlab/strand-braid

O_LISolitary bee species that use artificial trap nests are important for agricultural crop production and as indicators of habitat quality. Quantifying cavity-nesting solitary bee foraging and nesting behavior is essential for real-time analysis of population numbers and pollination activity, as well as understanding how environmental conditions shape reproductive success and population dynamics. However, manual observation is labor-intensive, prone to observer bias, and unable to deliver continuous data. Existing automated systems either require individual bee marking or detect presence without resolving nest-tube-level entry and exit events. C_LIO_LIWe developed BeeMonitor, an integrated hardware and computer-vision pipeline that detects nest entry and exit events in cavity-nesting solitary bees from continuous video, using Osmia cornifrons (the horn-faced mason bee) as a model system. A low-cost Raspberry Pi handles solar-powered field recording, while the software combines object detection (YOLOv26), a custom multiple-object tracker (BeeTrack), and a Random Forest classifier trained on trajectory-derived features to distinguish genuine events from incidental detections. C_LIO_LIOver a 29-day deployment, hardware reliability averaged 97.5% recording coverage. The pipeline achieved 91.3% precision and 87.3% recall (F1 = 0.893), generalizing robustly under leave-one-video-out cross-validation (mean F1 = 0.904). Detected foraging trips correlated strongly with brood cell counts (R2 = 0.849, p < 0.001, n = 19), and a Random Forest model (AUC = 0.820) identified solar radiation as the dominant driver of foraging activity, followed by temperature. C_LIO_LIBeeMonitor demonstrates that automated computer vision can reliably extract ecologically relevant behavioral data from continuous video, enabling real-time analysis of pollinator behavior and abundance at a temporal and spatial resolution unattainable through manual observation. Its modular design supports adaptation to other species and monitoring contexts. C_LI

We present three quantitative methods: 1) estimation of exoskeleton mechanical power and energy ratio from published data, 2) a systematic review of the exoskeleton literature on reported energy ratios, and 3) timing correction analysis of the replication experiment, to address concerns raised by Collins et al. (2026) about Luo et al. (2024). Together, these analyses support the reported metabolic reductions and the validity of exoskeleton control via learning in simulation. The critique rests on an unsupported premise: that exoskeleton energy ratios above 4 are physiologically implausible. This premise of Collins et al. (2026) is not supported by the cited evidence, and the error originates in their own cited source. Sawicki and Ferris (2009), the paper they invoke as authority for the limit of 4, state explicitly that "reported values of the muscular efficiency range from 0.10 to 0.34, with many sources assuming an average of [~]0.25." The value of 4 corresponds to this average, it is not a physiological ceiling. Treating an average as a physiological upper limit is a fundamental error. The published exoskeleton literature further contradicts the claim, including work by the authors of the critique themselves (Collins et al., 2015: 4.3; Young et al., 2017: 5.0) and independent work (Malcolm et al., 2013: 4.8; Seo et al., 2017: 6.7). In contrast, our walking energy ratio is 2.4, calculated directly from Fig. 4 of our paper. Our device delivers higher peak torque (14.1 Nm vs. 10.9 Nm, Lim et al., 2019) and achieves a slightly larger metabolic reduction (24.3% vs. 21%). Independent groups have since demonstrated meaningful metabolic reductions using learning-in-simulation frameworks, including Barati et al. (2026, 15.2% mean and 22.5% maximum) and Zhou et al. (2025, [~]20% during running). The claim of Collins et al. (2026) that this problem "remains unsolved" is directly contradicted by these independent results. The experiment in the critique is not a valid replication of our method. Our controller is a neural network with [~]10,000 parameters learned through deep reinforcement learning in musculoskeletal simulation; the critique instead applies a pre-programmed fixed torque curve with no learnable parameters. Beyond this, the replication contains three methodological errors: 1) a heel-strike timing assumption producing offsets up to 30% of the gait cycle; 2) an averaged torque profile that discards subject-specific control; and 3) a device [~]50% heavier than ours (4.8 kg vs. 3.2 kg) without measuring the metabolic penalty of the added weight. The critique also misreports Samsung data, with reported values approximately double those in the original publication, errors that directly underpin their physiological limit argument.

Human-in-the-loop optimization (HILO) is an established method for identifying subject-specific optimal controllers for performance augmentation. For HILO algorithms to be useful in rehabilitation, however, the optimization algorithm may need to account for how the human response changes over time in response to assistance. In this study, we tested a modified version of Bayesian optimization (BO), dynamic Bayesian optimization (DBO), in a three-parameter optimization problem that sought to identify participant-specific optimal solutions for increasing walking speed. As opposed to BO, DBO accounts for the non-stationarity of human responses. Sixteen healthy participants received bilateral hip torque pulses delivered by a hip exoskeleton. The exoskeleton torque parameters were determined using HILO with either DBO or BO. Validation iterations were introduced to objectively compare performance across optimizers at different time points of HILO. The results showed that both DBO and BO significantly increased walking speed compared to baseline. When comparing performance between DBO and BO, DBO emerged as an improvement over BO both in terms of efficacy, modeling accuracy, and personalization. DBO induced changes in walking speed relative to baseline that exceeded those induced by BO at three of the four validation iterations. DBO outperformed BO in modeling accuracy in later validation iterations. DBO personalization induced changes in walking speed that were significantly greater than those induced by previously identified assistive solutions, while this was not the case of BO. Overall, our results indicate that DBO outperformed BO due to its greater ability to account for non-stationary aspects of the human response.

Dung beetles can use a variety of orientation cues to maintain a consistent bearing during ball-rolling. Where several cues are available, they appear to learn the spatial relationship between them, providing redundancy if some cues are removed. Mounting evidence indicates that such a learning process is implemented in the insect head direction circuit; specifically, in the plastic substrate between sensory input neurons and compass neurons in the central complex. This plasticity appears to be driven by rotational movements, providing a clear link with observed beetle 'dance' behaviour. Here, we extend our functional model of this circuit and use it on a robot platform, to test it in the same behavioural assay as was used for the beetles. The robot was able to replicate the beetle's ability to substitute a directional wind cue for a point source light cue in guiding straight-line movement. However, it also revealed significant biasing coupled to dance direction. This biasing appears to be caused by inherent conflict between recurrent and instantaneous inputs to the compass circuit. We predict that the real insect should experience similar issues unless it has evolved a neural mechanism to compensate.

Many people which are affected by drop foot syndrome, have to face difficulty while walking which leads to pathological gait. This type of syndrome is treated by means of an external artificial stimulation known as functional electric stimulator (FES). In this paper we are designing an online feedback control system which optimize the strength of a FES given to paretic muscle which results in correction of pathological gait of the patient in a tolerable domain. Different phases of gait are identified using inertial measurement unit (IMU) as a feedback sensor mounted on the foot. Data is collected form 8 different healthy subjects and average of collected data is used as a reference template. Different trajectories of drop foot patients are simulated (due to unavailability of patients) and corrected according to the reference template.

Older adults face an increased risk of falls that may have severe consequences for their well-being. Routine, accessible clinical screening may help mitigate fall risk through early detection of balance impairments. Portable force plates offer a convenient and practical solution for balance assessment in clinical settings. A new force-plate-based balance measure, the intersection-point-height, has shown particularly promising results in its ability to distinguish between healthy and impaired balance behaviors. However, the intersection-point-height measure requires measurement of shear force during standing, which exhibits magnitudes of less than 0.2% of normal forces (body weight), taxing the dynamic range of most sensor technologies. The ability of existing force plates to measure such low-magnitude shear forces observed during quiet standing is currently unknown. This study presents a force-plate performance assessment method to evaluate shear-force measurement errors and quantify the uncertainty of the intersection-point-height measure. The method was applied to test a commonly used laboratory-grade portable force plate. While the device successfully captured sagittal-plane intersection-point-height at the lowest frequencies, low signal strength prevented precise readings in the frontal plane. Thus, the tested device only marginally met the precision required for quiet-standing analysis, underscoring the critical need for systematic performance validation of portable force plates prior to clinical use. Future efforts should focus on evaluating alternative portable force plates and exploring economical design improvements to enhance shear-force measurement precision.

Developing robust methods to quantify how animals allocate time across behaviours is essential for understanding energy use, habitat requirements, and responses to environmental change. For cryptic, semi-aquatic mammals such as the platypus, direct observation is difficult, creating a reliance on remote biologging approaches that can reliably infer behaviour in the wild. However, aquatic environments can both smooth acceleration signals through hydrodynamic damping and introduce noise from water movement, turbulence, and drag, potentially obscuring behavioural differences of similar magnitudes. We tested whether progressively incorporating biomechanical and frequency-domain (FFT-derived) predictors improved behavioural classification in hydrodynamically challenging aquatic environments. Tri-axial accelerometers were deployed on four ex situ platypuses, with synchronised video observations used to validate behaviour. From the acceleration data, we derived three predictor classes of increasing complexity: summary statistics describing activity level, engineered biomechanical variables capturing posture and body orientation, and FFT-derived features describing movement rhythm. These predictors were progressively incorporated into Random Forest models to classify five behaviours: burrow resting, surface resting, grooming, travelling/foraging, and diving. Model performance improved with increasing predictor complexity, although gains were behaviour specific. FFT-derived features substantially improved classification of rhythmic behaviours such as diving and foraging, while engineered biomechanical predictors improved grooming detection. In contrast, resting behaviours, particularly surface resting, showed little improvement. Overall accuracy increased from [~]75% to [~]88% when frequency-domain features were included. Misclassification was greatest among behaviours with overlapping or low-amplitude signals, and cross-individual validation revealed reduced model generalisability, indicating that individual variation in movement patterns constrained transferability. Incorporating frequency-domain features substantially improved behavioural classification in platypuses, particularly for rhythmic behaviours such as diving and foraging. This study provides the first validated accelerometry-based behavioural classification framework for the species and highlights the importance of matching predictor selection to behavioural mechanics. More broadly, the approach offers a transferable framework for aquatic and semi-aquatic taxa.

Cruising speed is a key factor affecting prey-search efficiency and migration range in continuously swimming animals. Tunas and lamnid sharks (e.g., white sharks) have convergently evolved traits for high-speed cruising, including the ability to maintain slow-twitch, aerobic red muscle (RM) warmer than ambient water, known as RM endothermy. Despite their well-known high cruising speeds, kinematic features underlying their elevated speeds remain unclear. Swim speed is the product of tailbeat frequency (TBF; Hz) and stride length (SL, the absolute distance traveled per tailbeat; m). RM endothermy is expected to elevate TBF by enhancing muscle contraction performance. Furthermore, within RM-endothermic fishes, tunas and lamnid sharks may exhibit distinct kinematic features because of differences in caudal fin morphology and tailbeat amplitude. Here, we compiled kinematic parameters from 20 fish species, including five RM-endothermic species, measured in the wild using animal-borne sensors. Comparative analyses showed that, for a given body mass and water temperature, RM-endothermic fishes exhibited 1.9 times higher cruising speed and TBF than ectothermic fishes, while SL remained similar. Within RM-endothermic fishes, tunas exhibited 2.3 times higher TBF than similar-sized lamnid sharks, whereas lamnid sharks showed 1.7 times longer SL than similar-sized tunas. These results indicate that RM endothermy is generally associated with higher TBF, while significant kinematic differences remain between tunas and lamnid sharks. This divergence may be partly explained by the greater caudal fin area and tailbeat amplitude in lamnid sharks. It may also reflect contrasting skeletal types of teleosts and elasmobranchs, which potentially influence body stiffness and swimming kinematics.

Animals often rely on social information when making movement decisions. In zebrafish, classic work showed that shoal size and shoal activity both bias shoal choice. Here we extend these effects in Goldfish (Carassius auratus) and extend them with a drift-diffusion model (DDM) account of individual evidence accumulation under dynamic social cues. Using a three-chamber linear arena, we quantified a focal fishs position for 10 minutes while manipulating (i) numerical differences between flanking shoals and (ii) their activity (swimming speed) via temperature manipulation. ANOVA on time-proportion choices confirmed robust attraction to larger shoals; when shoal sizes were equal, the more active shoal was preferred. In combined manipulations, activity effects dominated at small numbers but saturated as group size increased, indicating a threshold-like integration where activity dominates at small shoal sizes (<3 fish) but saturates at larger sizes. We formalize these processes with a bounded DDM in which a sigmoidal stimulus function maps shoal size and average speed to momentary evidence, subject to random perturbations. The model reproduces the observed psychometric relations between relative numerosity, velocity differences, and choice. Our results (i) generalize zebrafish findings to a carp species with distinct ecology and physiology, and (ii) provide a compact mechanistic link between social cues and individual decision trajectories in dynamic social contexts.

Physical human-device interaction is central to many emerging technologies in neurorehabilitation and assistive robotics, but simulation-based research in this area remains fragmented across musculoskeletal models, assistive-device representations, task definitions, and controller-development workflows. This fragmentation limits the accessibility, reproducibility, and extensibility of studies on prostheses, exoskeletons, wearable rehabilitation devices, and related human-device systems. Here we introduce MyoAssist 1.0, an open-source framework for neuromechanical simulation of physical human-device interaction built within the MyoSuite ecosystem. MyoAssist organizes each simulation environment as a composed human-device-task system that combines compatible musculoskeletal, assistive-device, and task-scenario components through a shared composition pipeline. The current release includes 15 assistive-device models spanning gait assistance, upper-body support, manipulation, and seated mobility and supports compatible musculoskeletal models ranging from reduced lower-limb models to a 416-muscle full-body model. These human-device systems can be simulated within the broad task scenarios provided by MyoSuite, while MyoAssist adds locomotion-specific task scenarios with configurable terrain and target-velocity conditions for gait-assistive studies. MyoAssist also provides two complementary controller-development frameworks: a reinforcement-learning framework for training adaptive policies and a controller-optimization framework for tuning structured, interpretable human and device controllers. Both frameworks operate on the same simulation environments and provide standardized evaluation outputs for inspecting, comparing, reusing, and extending learned and structured control strategies. By integrating modular human models, assistive-device models, task scenarios, and training workflows under a shared open-source interface, MyoAssist aims to lower the barrier to reproducible simulation-based research and to support collaborative development of assistive technologies for neurorehabilitation and physical human-device interaction.

PurposeAnkle stiffness can be altered by normal aging, bone and joint pathology, and treatments such as orthoses or surgical joint fusion. The effects of ankle stiffness on gait are not yet well understood but may be crucial for understanding how these pathologies and treatments influence body mechanics. The objective of this work was to investigate how isolated changes in stiffness applied in parallel with the ankle impact lower-limb kinematics, kinetics, joint work, and muscle activation during walking in individuals without lower-limb pathology. MethodsNine young adults without lower-limb pathology wore an adjustable-stiffness ankle exoskeleton and walked at 31 different conditions of ankle spring stiffness, neutral angle, and treadmill incline. We recorded motion capture data, ground reaction forces, and muscle activation, and analyzed the resultant data for trends as a function of ankle stiffness. ResultsExoskeleton-side ankle range of motion decreased and asymmetry increased across all joints as ankle stiffness increased, primarily due to decreased plantarflexion at toe-off. The 30 Nm/rad spring stiffness condition led to a minimum in mean exoskeleton-side muscle activation and hip joint work, but increased kinematic asymmetry. ConclusionOur results suggest that there may exist a range of stiffnesses at the lower end of typically-studied values that can reduce muscle activation and joint work during walking, though at the cost of kinematic symmetry. These findings provide a deeper understanding of how ankle stiffness influences gait mechanics, with potential applications in wearable devices, clinical rehabilitation, and assistive technology.

Extensible body structures have evolved repeatedly across animals, yet the mechanisms underlying the deployment of extensible organs often remain unknown. Eristalinae hoverfly larvae (rat tailed maggots) possess exceptionally elongated posterior respiratory siphons, but the mechanism underlying their extension has not been experimentally investigated. Here, using wild collected Helophilus virgatus larvae, we show that posterior siphon extension is achieved through a folding unfolding mechanism revealed by fluorescence labeling. Phalloidin staining further demonstrated that, unlike Episyrphus sp. and Drosophila melanogaster, H. virgatus possesses a dense array of transversely oriented muscle fibers in the posterior siphon. Behavioral analyses further revealed that the posterior siphon functions not only in respiration but also as a propulsive organ for near surface locomotion through asymmetric rowing. Together, our findings identify the structural and kinematic basis of posterior siphon deployment and demonstrate how a specialized respiratory organ can evolve into a multifunctional appendage that supports both respiration and locomotion.

Buzz pollination is an important behavior in which bees use vibrations to extract pollen from poricidal anthers. However, the extent to which vibration frequency influences pollen release remains unclear. Here, we quantified pollen expulsion from Solanum sisymbriifolium anthers subjected to harmonic excitation over a broad frequency range encompassing the anthers first natural frequency. We excited anthers to expel pollen and measured anther kinematics and pollen release using high-speed videography. Particle tracking enabled continuous estimation of pollen release throughout each buzzing event, allowing both initial pollen flux and total pollen released to be quantified. Pollen release depended strongly on excitation frequency. Initial pollen flux, total pollen release, and anther kinematics peaked when excitation frequency approached the anthers natural frequency. Anther tip velocity amplitude exhibited the strongest correlation with total pollen release (r = 0.755) and initial pollen flux (r = 0.898). Experimental observations were compared with nonlinear and linear statistical models of pollen release. While both models captured trends in normalized pollen flux, they overpredicted total pollen release, suggesting that adhesive interactions play important roles during extended buzzing events. These findings demonstrate that anther structural dynamics influence pollen release and suggest that vibration amplification may improve the efficiency of buzz pollination.

Predator-prey interactions shape the evolution of escape behavior in prey, including different combinations of evasive movements, that may enhance unpredictability in fleeing directions and trajectories. So-called protean motion can enhance survival of flying prey in the wild, but quantifying such behaviors under natural conditions remains challenging. Here we used stereoscopic high-speed videography to record the escape flight behavior of wild males of the butterfly species Morpho menelaus in the Amazonian rainforest, and reconstructed 3D flight trajectories using artificial-neural-network-based tracking. During the experiments, we used a lure to attract freely patrolling male butterflies and elicited escape flights by intercepting their trajectory with a looming insect net swing. We then compared the escape flight kinematics to the pre-attack patrolling behavior. Attacks first induced a rapid upward maneuvering, directly followed by an unpredictable horizontal turn. The following escape flight trajectories showed increased horizontal erraticity and greater intra-individual heading variability, as compared to the pre-attack flight. Surprisingly, the mean speed decreased in the escape phase, notably in the horizontal plane. A significant negative association between horizontal trajectory complexity and flight speed was detected, indicating a speed-erraticity trade-off. These results show that wild Morpho butterflies respond to attacks by combining a climbing maneuver with an unpredictable heading change, followed by a protean escape flight; this increased escape erraticity comes at the expense of reduced escape flight speed. Because these large and relatively slow-flying butterflies display bright iridescent blue coloration on their dorsal wing side, erraticity during flight might enhance the dynamic flash coloration, likely limiting accurate targeting by predators.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.