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.

Visual versus visual-inertial guidance in hawks pursuing terrestrial targets.

The aerial interception behaviour of falcons is well modelled by a guidance law called proportional navigation, which commands steering at a rate proportional to the angular rate of the line-of-sight from predator to prey. Because the line-of-sight rate is defined in an inertial frame of reference, proportional navigation must be implemented using visual-inertial sensor fusion. By contrast, the aerial pursuit behaviour of hawks chasing terrestrial targets is better modelled by a mixed guidance law combining information on the line-of-sight rate with information on the deviation angle between the attacker's velocity and the line-of-sight. Here we ask whether this behaviour may be controlled using visual information alone. We use high-speed motion capture to record n = 228 flights from N = 4 Harris' hawks Parabuteo unicinctus, and show that proportional navigation and mixed guidance both model their trajectories well. The mixed guidance law also models the data closely when visual-inertial information on the line-of-sight rate is replaced by visual information on the motion of the target relative to its background. Although the visual-inertial form of the mixed guidance law provides the closest fit, all three guidance laws provide an adequate phenomenological model of the behavioural data, whilst making different predictions on the physiological pathways involved.

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.

Optimization of avian perching manoeuvres.

Perching at speed is among the most demanding flight behaviours that birds perform1,2 and is beyond the capability of most autonomous vehicles. Smaller birds may touch down by hovering3-8, but larger birds typically swoop up to perch1,2-presumably because the adverse scaling of their power margin prohibits hovering9 and because swooping upwards transfers kinetic to potential energy before collision1,2,10. Perching demands precise control of velocity and pose11-14, particularly in larger birds for which scale effects make collisions especially hazardous6,15. However, whereas cruising behaviours such as migration and commuting typically minimize the cost of transport or time of flight16, the optimization of such unsteady flight manoeuvres remains largely unexplored7,17. Here we show that the swooping trajectories of perching Harris' hawks (Parabuteo unicinctus) minimize neither time nor energy alone, but rather minimize the distance flown after stalling. By combining motion capture data from 1,576 flights with flight dynamics modelling, we find that the birds' choice of where to transition from powered dive to unpowered climb minimizes the distance over which high lift coefficients are required. Time and energy are therefore invested to provide the control authority needed to glide safely to the perch, rather than being minimized directly as in technical implementations of autonomous perching under nonlinear feedback control12 and deep reinforcement learning18,19. Naive birds learn this behaviour on the fly, so our findings suggest a heuristic principle that could guide reinforcement learning of autonomous perching.

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.

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

Aerial predators adopt a variety of different hunting styles, with divergent flight morphologies typically adapted either to high-speed interception or manoeuvring through clutter, but how are their sensorimotor systems tuned in relation to habitat structure and prey behavior? Falcons intercept prey at high-speed using the same proportional navigation guidance law as homing missiles. This classical guidance law works well in the open, but performs sub-optimally against highly-manoeuvrable targets, and may not produce a feasible path through the cluttered environments frequented by hawks and other raptors. Here we identify the guidance law of n = 5 Harris' Hawks Parabuteo unicinctus chasing erratically manoeuvring artificial targets. Harris' Hawks use a mixed guidance law, coupling low-gain proportional navigation with a low-gain proportional pursuit element. This guidance law promotes tail-chasing and is not thrown off by erratic manoeuvres, making it well suited to the hawks' natural hunting style, involving close pursuit of agile prey through clutter.

Terminal attack trajectories of peregrine falcons are described by the proportional navigation guidance law of missiles.

The ability to intercept uncooperative targets is key to many diverse flight behaviors, from courtship to predation. Previous research has looked for simple geometric rules describing the attack trajectories of animals, but the underlying feedback laws have remained obscure. Here, we use GPS loggers and onboard video cameras to study peregrine falcons, Falco peregrinus, attacking stationary targets, maneuvering targets, and live prey. We show that the terminal attack trajectories of peregrines are not described by any simple geometric rule as previously claimed, and instead use system identification techniques to fit a phenomenological model of the dynamical system generating the observed trajectories. We find that these trajectories are best-and exceedingly well-modeled by the proportional navigation (PN) guidance law used by most guided missiles. Under this guidance law, turning is commanded at a rate proportional to the angular rate of the line-of-sight between the attacker and its target, with a constant of proportionality (i.e., feedback gain) called the navigation constant (N). Whereas most guided missiles use navigation constants falling on the interval 3 ≤ N ≤ 5, peregrine attack trajectories are best fitted by lower navigation constants (median N < 3). This lower feedback gain is appropriate at the lower flight speed of a biological system, given its presumably higher error and longer delay. This same guidance law could find use in small visually guided drones designed to remove other drones from protected airspace.

Critical role for protein kinase A in the acquisition of gregarious behavior in the desert locust.

The mechanisms that integrate genetic and environmental information to coordinate the expression of complex phenotypes are little understood. We investigated the role of two protein kinases (PKs) in the population density-dependent transition to gregarious behavior that underlies swarm formation in desert locusts: the foraging gene product, a cGMP-dependent PK (PKG) implicated in switching between alternative group-related behaviors in several animal species; and cAMP-dependent PK (PKA), a signal transduction protein with a preeminent role in different forms of learning. Solitarious locusts acquire key behavioral characters of the swarming gregarious phase within just 1 to 4 h of forced crowding. Injecting the PKA inhibitor KT5720 before crowding prevented this transition, whereas injecting KT5823, an inhibitor of PKG, did not. Neither drug altered the behavior of long-term gregarious locusts. RNAi against foraging effectively reduced its expression in the central nervous system, but this did not prevent gregarization upon crowding. By contrast, solitarious locusts with an RNAi-induced reduction in PKA catalytic subunit C1 expression behaved less gregariously after crowding, and RNAi against the inhibitory R1 subunit promoted more extensive gregarization following a brief crowding period. A central role of PKA is congruent with the recent discovery that serotonin mediates gregarization in locusts and with findings in vertebrates that similarly implicate PKA in the capacity to cope with adverse life events. Our results show that PKA has been coopted into effecting the wide-ranging transformation from solitarious to gregarious behavior, with PKA-mediated behavioral plasticity resulting in an environmentally driven reorganization of a complex phenotype.