Data from: 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.拦截非合作目标的能力，是从求偶到捕食等多种飞行行为的核心要素。过往研究曾试图寻找描述动物攻击轨迹的简单几何规则，但背后的反馈定律始终不明晰。本研究通过GPS记录仪与机载摄像机，对游隼（*Falco peregrinus*）攻击静止目标、机动目标与活体猎物的过程展开研究。结果表明，游隼的末端攻击轨迹并不符合此前宣称的任何简单几何规则；为此我们采用系统辨识技术，为生成观测轨迹的动力学系统拟合得到一个现象学模型。我们发现，这类轨迹可通过大多数制导导弹所采用的比例导航（Proportional Navigation, PN）制导律得到极佳且极高精度的拟合。该制导律下，飞行器的转向角速度与攻击者和目标间视线的角速度成正比，该比例系数（即反馈增益）被称为导航常数（N）。尽管多数制导导弹的导航常数取值区间为3≤N≤5，但游隼的攻击轨迹最优拟合结果对应的导航常数更低（中位数N<3）。考虑到生物系统普遍存在更高的误差与更长的延迟，较低的反馈增益适配其更低的飞行速度。该制导律同样可应用于小型视觉制导无人机，用于将其他无人机驱离受保护空域。