قارن الطرق

	مسار دوبنز (Dubins Path)	الملاحة النسبية	تمثيل الاتجاه بالرباعيات
المجال	هندسة الطيران والفضاء	هندسة الطيران والفضاء	هندسة الطيران والفضاء
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1957	1957	1843
صاحب الطريقة	Lester Dubins	Lin-Hsiung Chu	William Hamilton (quaternions), aerospace engineers
النوع	Optimal curve	Guidance law	Mathematical framework
المصدر التأسيسي	Dubins, L. E. (1957). On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents. American Journal of Mathematics, 79(3), 497–516.	Knox, W. P. (1971). On optimal proportional navigation. IEEE Transactions on Aerospace and Electronic Systems, AES-7(3), 417–426.	Shuster, M. D. (1993). A survey of attitude representations. Journal of the Astronautical Sciences, 41(4), 439–517.
الأسماء البديلة	Dubins curve, RSR path, LSL path	PN, PN law	quaternion representation, attitude kinematics, q-vector
ذات صلة	3	3	3
الملخص	The Dubins path is the shortest curve connecting two points in the plane with prescribed initial and terminal tangent directions, subject to a constraint on curvature. Introduced by Lester Dubins in 1957, it solved a fundamental problem in differential geometry and became essential in motion planning for aircraft, helicopters, and autonomous vehicles. A Dubins path consists of circular arcs and straight line segments arranged in a sequence such as RSR (Right-Straight-Right) or LSL (Left-Straight-Left).	Proportional Navigation (PN) is a guidance law that generates command accelerations proportional to the rate of change of the line-of-sight angle between a pursuer and target. Introduced by Lin-Hsiung Chu in the 1950s, it became the foundation of modern missile guidance systems. PN solves the pursuit-evasion problem by ensuring that the pursuer intercepts a moving target with minimal computational overhead.	Quaternion attitude representation is a mathematical framework for describing three-dimensional rotations using four-dimensional vectors (quaternions). Superior to Euler angles due to the absence of singularities (gimbal lock), quaternions are the standard representation in modern attitude estimation, spacecraft control, and 3D computer graphics. Quaternion kinematics elegantly expresses how attitude evolves under angular velocity measurements from gyroscopes.