Hawks steer attacks using a guidance system tuned for close pursuit of erratically manoeuvring targets

An ethologically motivated neurobiology of primate visually-guided reach-to-grasp behavior

The precision of primate visually guided reaching likely evolved to meet the many challenges faced by living in arboreal environments, yet much of what we know about the underlying primate brain organization derives from a set of highly constrained experimental paradigms. Here we review the role of vision to guide natural reach-to-grasp movements in marmoset monkey prey capture to illustrate the breadth and diversity of these behaviors in ethological contexts, the fast predictive nature of these movements [1,2], and the advantages of this particular primate model to investigate the underlying neural mechanisms in more naturalistic contexts [3]. In addition to their amenability to freely-moving neural recording methods for investigating the neural basis of dynamic ethological behaviors [4,5], marmosets have a smooth neocortical surface that facilitates imaging and array recordings [6,7] in all areas in the primate fronto-parietal network [8,9]. Together, this model organism offers novel opportunities to study the real-world interplay between primate vision and reach-to-grasp dynamics using ethologically motivated neuroscientific experimental designs.

Multiplayer Reach-Avoid Differential Games in 3D Space Inspired by Harris' Hawks' Cooperative Hunting Tactics

This paper investigates a multiplayer reach-avoid differential game in 3-dimensional (3D) space, which involves multiple pursuers, multiple evaders, and a designated target region. The evaders aim to reach the target region, while the pursuers attempt to guard the target region by capturing the evaders. This class of research holds significant practical value. However, the complexity of the problem escalates substantially with the growing number of players, rendering its solution extremely challenging. In this paper, the multiplayer game is divided into many subgames considering the cooperation among pursuers, reducing the computational burden, and obtaining numerically tractable strategies for players. First, the Apollonius sphere, a fundamental geometric tool for analyzing the 3D differential game, is formulated, and its properties are proved. Based on this, the optimal interception point for the pursuer to capture the evader is derived and the winning conditions for the pursuer and evader are established. Then, based on the Apollonius sphere, the optimal state feedback strategies of players are designed, and simultaneously, the optimal one-to-one pairings are obtained. Meanwhile, the Value function of the multiplayer reach-avoid differential game is explicitly given and is proved to satisfy Hamilton-Jacobi-Isaacs (HJI) equation. Moreover, the matching algorithm for the case with pursuers outnumbered evaders is provided through constructing a weighted bipartite graph, and the cooperative tactics for multiple pursuers are proposed, inspired by the Harris' Hawks intelligent cooperative hunting tactics. Finally, numerical simulations are conducted to illustrate the effectiveness of the theoretical results for both cases where the number of adversary players is equal and unequal between the 2 groups.

Obstacle avoidance in aerial pursuit

Pursuing prey through clutter is a complex and risky activity requiring integration of guidance subsystems for obstacle avoidance and target pursuit. The unobstructed pursuit trajectories of Harris' hawks Parabuteo unicinctus are well modeled by a mixed guidance law feeding back target deviation angle and line-of-sight rate. Here we ask how their pursuit behavior is modified in response to obstacles, using high-speed motion capture to reconstruct flight trajectories recorded during obstructed pursuit of maneuvering targets. We find that Harris' hawks use the same mixed guidance law during obstructed pursuit but appear to superpose a discrete bias command that resets their flight direction to aim at a clearance of approximately one wing length from an upcoming obstacle as they reach some threshold distance from it. Combining a feedback command in response to target motion with a feedforward command in response to upcoming obstacles provides an effective means of prioritizing obstacle avoidance while remaining locked-on to a target. We therefore anticipate that a similar mechanism may be used in terrestrial and aquatic pursuit. The same biased guidance law could also be used for obstacle avoidance in drones designed to intercept other drones in clutter, or to navigate between fixed waypoints in urban environments.

Strategic predatory pursuit of the stealthy, highly manoeuvrable, slow flying bat Corynorhinus townsendii

A predator's capacity to catch prey depends on its ability to navigate its environment in response to prey movements or escape behaviour. In predator-prey interactions that involve an active chase, pursuit behaviour can be studied as the collection of rules that dictate how a predator should steer to capture prey. It remains unclear how variable this behaviour is within and across species since most studies have detailed the pursuit behaviour of high-speed, open-area foragers. In this study, we analyse the pursuit behaviour in 44 successful captures by Corynorhinus townsendii, Townsend's big-eared bat (n = 4). This species forages close to vegetation using slow and highly manoeuvrable flight, which contrasts with the locomotor capabilities and feeding ecologies of other taxa studied to date. Our results indicate that this species relies on an initial stealthy approach, which is generally sufficient to capture prey (32 out of 44 trials). In cases where the initial approach is not sufficient to perform a capture attempt (12 out of 44 trials), C. townsendii continues its pursuit by reacting to prey movements in a manner best modelled with a combination of pure pursuit, or following prey directly, and proportional navigation, or moving to an interception point.

Fast prediction in marmoset reach-to-grasp movements for dynamic prey

Primates have evolved sophisticated, visually guided reaching behaviors for interacting with dynamic objects, such as insects, during foraging.1,2,3,4,5 Reaching control in dynamic natural conditions requires active prediction of the target's future position to compensate for visuo-motor processing delays and to enhance online movement adjustments.6,7,8,9,10,11,12 Past reaching research in non-human primates mainly focused on seated subjects engaged in repeated ballistic arm movements to either stationary targets or targets that instantaneously change position during the movement.13,14,15,16,17 However, those approaches impose task constraints that limit the natural dynamics of reaching. A recent field study in marmoset monkeys highlights predictive aspects of visually guided reaching during insect prey capture among wild marmoset monkeys.5 To examine the complementary dynamics of similar natural behavior within a laboratory context, we developed an ecologically motivated, unrestrained reach-to-grasp task involving live crickets. We used multiple high-speed video cameras to capture the movements of common marmosets (Callithrix jacchus) and crickets stereoscopically and applied machine vision algorithms for marker-free object and hand tracking. Contrary to estimates under traditional constrained reaching paradigms, we find that reaching for dynamic targets can operate at incredibly short visuo-motor delays around 80 ms, rivaling the speeds that are typical of the oculomotor systems during closed-loop visual pursuit.18 Multivariate linear regression modeling of the kinematic relationships between the hand and cricket velocity revealed that predictions of the expected future location can compensate for visuo-motor delays during fast reaching. These results suggest a critical role of visual prediction facilitating online movement adjustments for dynamic prey.

Through Hawks’ Eyes: Synthetically Reconstructing the Visual Field of a Bird in Flight

Birds of prey rely on vision to execute flight manoeuvres that are key to their survival, such as intercepting fast-moving targets or navigating through clutter. A better understanding of the role played by vision during these manoeuvres is not only relevant within the field of animal behaviour, but could also have applications for autonomous drones. In this paper, we present a novel method that uses computer vision tools to analyse the role of active vision in bird flight, and demonstrate its use to answer behavioural questions. Combining motion capture data from Harris’ hawks with a hybrid 3D model of the environment, we render RGB images, semantic maps, depth information and optic flow outputs that characterise the visual experience of the bird in flight. In contrast with previous approaches, our method allows us to consider different camera models and alternative gaze strategies for the purposes of hypothesis testing, allows us to consider visual input over the complete visual field of the bird, and is not limited by the technical specifications and performance of a head-mounted camera light enough to attach to a bird’s head in flight. We present pilot data from three sample flights: a pursuit flight, in which a hawk intercepts a moving target, and two obstacle avoidance flights. With this approach, we provide a reproducible method that facilitates the collection of large volumes of data across many individuals, opening up new avenues for data-driven models of animal behaviour.

Gap selection and steering during obstacle avoidance in pigeons

The ability of birds to fly through cluttered environments has inspired biologists interested in understanding its underlying mechanisms, and engineers interested in applying its underpinning principles. To analyse this problem empirically, we break it down into two distinct, but related, questions: How do birds select which gaps to aim for? And how do they steer through them? We answered these questions using a combined experimental and modelling approach, in which we released pigeons (Columbia livia domestica) inside a large hall with an open exit separated from the release point by a curtain creating two vertical gaps - one of which was obstructed by an obstacle. We tracked the birds using a high-speed motion capture system, and found that their gap choice seemed to be biased by their intrinsic handedness, rather than determined by extrinsic cues such as the size of the gap or its alignment with the destination. We modelled the pigeons' steering behaviour algorithmically by simulating their flight trajectories under a set of six candidate guidance laws, including those used previously to model target-oriented flight behaviours in birds. We found that their flights were best modelled by delayed proportional navigation commanding turning in proportion to the angular rate of the line-of-sight from the pigeon to the midpoint of the gap. Our results are consistent with this being a two-phase behaviour, in which the pigeon heads forward from the release point before steering towards the midpoint of whichever gap it chooses to aim for under closed-loop guidance. Our findings have implications for the sensorimotor mechanisms that underlie clutter negotiation in birds, uniting this with other kinds of target-oriented behaviours including aerial pursuit.

Raptors avoid the confusion effect by targeting fixed points in dense aerial prey aggregations

Collective behaviours are widely assumed to confuse predators, but empirical support for a confusion effect is often lacking, and its importance must depend on the predator’s targeting mechanism. Here we show that Swainson’s Hawks Buteo swainsoni and other raptors attacking swarming Mexican Free-tailed Bats Tadarida brasiliensis steer by turning towards a fixed point in space within the swarm, rather than by using closed-loop pursuit of any one individual. Any prey with which the predator is on a collision course will appear to remain on a constant bearing, so target selection emerges naturally from the geometry of a collision. Our results show how predators can simplify the demands on their sensory system by decoupling steering from target acquisition when capturing prey from a dense swarm. We anticipate that the same tactic will be used against flocks and schools across a wide range of taxa, in which case a confusion effect is paradoxically more likely to occur in attacks on sparse groups, for which steering and target acquisition cannot be decoupled.

Flocking, schooling, and swarming prey are thought to benefit from a confusion effect. However, here the authors show that hawks attacking swarming bats avoid confusion by steering towards a fixed point in the swarm instead of targeting any one individual.

Avoiding obstacles while intercepting a moving target: a miniature fly's solution

The miniature robber fly Holcocephala fusca intercepts its targets with behaviour that is approximated by the proportional navigation guidance law. During predatory trials, we challenged the interception of H. fusca performance by placing a large object in its potential flight path. In response, H. fusca deviated from the path predicted by pure proportional navigation, but in many cases still eventually contacted the target. We show that such flight deviations can be explained as the output of two competing navigational systems: pure-proportional navigation and a simple obstacle avoidance algorithm. Obstacle avoidance by H. fusca is here described by a simple feedback loop that uses the visual expansion of the approaching obstacle to mediate the magnitude of the turning-away response. We name the integration of this steering law with proportional navigation 'combined guidance'. The results demonstrate that predatory intent does not operate a monopoly on the fly's steering when attacking a target, and that simple guidance combinations can explain obstacle avoidance during interceptive tasks.

An Algorithmic Approach to Natural Behavior

Uncovering the mechanisms and implications of natural behavior is a goal that unites many fields of biology. Yet, the diversity, flexibility, and multi-scale nature of these behaviors often make understanding elusive. Here, we review studies of animal pursuit and evasion - two special classes of behavior where theory-driven experiments and new modeling techniques are beginning to uncover the general control principles underlying natural behavior. A key finding of these studies is that intricate sequences of pursuit and evasion behavior can often be constructed through simple, repeatable rules that link sensory input to motor output: we refer to these rules as behavioral algorithms. Identifying and mathematically characterizing these algorithms has led to important insights, including the discovery of guidance rules that attacking predators use to intercept mobile prey, and coordinated neural and biomechanical mechanisms that animals use to avoid impending collisions. Here, we argue that algorithms provide a good starting point for studies of natural behavior more generally. Rather than beginning at the neural or ecological levels of organization, we advocate starting in the middle, where the algorithms that link sensory input to behavioral output can provide a solid foundation from which to explore both the implementation and the ecological outcomes of behavior. We review insights that have been gained through such an algorithmic approach to pursuit and evasion behaviors. From these, we synthesize theoretical principles and lay out key modeling tools needed to apply an algorithmic approach to the study of other complex natural behaviors.

Gravity and active acceleration limit the ability of killer flies (Coenosia attenuata) to steer towards prey when attacking from above

Insects that predate aerially usually contrast prey against the sky and attack upwards. However, killer flies (Coenosia attenuata) can attack prey flying below them, performing what we term 'aerial dives'. During these dives, killer flies accelerate up to 36 m s-2. Although the trajectories of the killer fly's dives appear highly variable, proportional navigation explains them, as long as the model has the lateral acceleration limit of a real killer fly. The trajectory's steepness is explained by the initial geometry of engagement; steep attacks result from the killer fly taking off when the target is approaching the predator. Under such circumstances, the killer fly dives almost vertically towards the target, and gravity significantly increases its acceleration. Although killer flies usually time their take-off to minimize flight duration, during aerial dives killer flies cannot reach the lateral accelerations necessary to match the increase in speed caused by gravity. Since a close miss still leads the predator closer to the target, and might even slow the prey down, there may not be a selective pressure for killer flies to account for gravity during aerial dives.

Aerial attack strategies of hawks hunting bats, and the adaptive benefits of swarming

Aggregation can reduce an individual’s predation risk, by decreasing predator hunting efficiency or displacing predation onto others. Here, we explore how the behaviors of predator and prey influence catch success and predation risk in Swainson’s hawks Buteo swainsoni attacking swarming Brazilian free-tailed bats Tadarida brasiliensis on emergence. Lone bats including stragglers have a high relative risk of predation, representing ~5% of the catch but ~0.2% of the population. Attacks on the column were no less successful than attacks on lone bats, so hunting efficiency is not decreased by group vigilance or confusion. Instead, lone bats were attacked disproportionately often, representing ~10% of all attacks. Swarming therefore displaces the burden of predation onto bats outside the column—whether as isolated wanderers not benefitting from dilution through attack abatement, or as peripheral stragglers suffering marginal predation and possible selfish herd effects. In contrast, the hawks’ catch success depended only on the attack maneuvers that they employed, with the odds of success being more than trebled in attacks involving a high-speed stoop or rolling grab. Most attacks involved one of these two maneuvers, which therefore represent alternative rather than complementary tactics. Hence, whereas a bat’s survival depends on maintaining column formation, a hawk’s success does not depend on attacking lone bats—even though their tendency to do so is sufficient to explain the adaptive benefits of their prey’s aggregation behavior. A hawk’s success instead depends on the flight maneuvers it deploys, including the high-speed stoop that is characteristic of many raptors.

Swarming bats emerging from a massive desert roost reduce their predation risk by maintaining tight column formation, because the hawks that predate them attack peripheral stragglers and isolated wanderers disproportionately. Whereas a bat’s predation risk depends on maintaining its position within the column, the catch success of a hawk depends on how it maneuvers itself to attack, and is maximized by executing a high-speed dive or rolling grab maneuver.

Attack behaviour in naive gyrfalcons is modelled by the same guidance law as in peregrine falcons, but at a lower guidance gain

The aerial hunting behaviours of birds are strongly influenced by flight morphology and ecology, but little is known of how this relates to the behavioural algorithms guiding flight. Here, we used GPS loggers to record the attack trajectories of captive-bred gyrfalcons (Falco rusticolus) during their maiden flights against robotic aerial targets, which we compared with existing flight data from peregrine falcons (Falco peregrinus). The attack trajectories of both species were well modelled by a proportional navigation (PN) guidance law, which commands turning in proportion to the angular rate of the line-of-sight to target, at a guidance gain N However, naive gyrfalcons operate at significantly lower values of N than peregrine falcons, producing slower turning and a longer path to intercept. Gyrfalcons are less manoeuvrable than peregrine falcons, but physical constraint is insufficient to explain the lower values of N we found, which may reflect either the inexperience of the individual birds or ecological adaptation at the species level. For example, low values of N promote the tail-chasing behaviour that is typical of wild gyrfalcons and which apparently serves to tire their prey in a prolonged high-speed pursuit. Likewise, during close pursuit of typical fast evasive prey, PN will be less prone to being thrown off by erratic target manoeuvres at low guidance gain. The fact that low-gain PN successfully models the maiden attack flights of gyrfalcons suggests that this behavioural algorithm is embedded in a guidance pathway ancestral to the clade containing gyrfalcons and peregrine falcons, though perhaps with much deeper evolutionary origins.

Two pursuit strategies for a single sensorimotor control task in blowfly

Effective visuomotor coordination is a necessary requirement for the survival of many terrestrial, aquatic, and aerial animal species. We studied the kinematics of aerial pursuit in the blowfly Lucilia sericata using an actuated dummy as target for freely flying males. We found that the flies perform target tracking in the horizontal plane and target interception in the vertical plane. Our behavioural data suggest that the flies’ trajectory changes are a controlled combination of target heading angle and of the rate of change of the bearing angle. We implemented control laws in kinematic models and found that the contributions of proportional navigation strategy are negligible. We concluded that the difference between horizontal and vertical control relates to the difference in target heading angle the fly keeps constant: 0° in azimuth and 23° in elevation. Our work suggests that male Lucilia control both horizontal and vertical steerings by employing proportional controllers to the error angles. In horizontal plane, this controller operates at time delays as small as 10 ms, the fastest steering response observed in any flying animal, so far.