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	Ścieżka Dubinsa	AHRS	Kwaternionowe położenie
Dziedzina	Lotnictwo i kosmonautyka	Lotnictwo i kosmonautyka	Lotnictwo i kosmonautyka
Rodzina	Process / pipeline	Process / pipeline	Process / pipeline
Rok powstania	1957	1940s	1843
Twórca	Lester Dubins	Aviation heritage	William Hamilton (quaternions), aerospace engineers
Typ	Optimal curve	System	Mathematical framework
Źródło pierwotne	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.	Savage, P. G. (2007). Strapdown Inertial Integration Technology (2nd ed.). Strapdown Associates.	Shuster, M. D. (1993). A survey of attitude representations. Journal of the Astronautical Sciences, 41(4), 439–517.
Inne nazwy	Dubins curve, RSR path, LSL path	AHRS system, attitude reference, heading sensor	quaternion representation, attitude kinematics, q-vector
Pokrewne	3	3	3
Podsumowanie	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).	An Attitude Heading Reference System (AHRS) is a complete inertial navigation subsystem that estimates and outputs the three-dimensional orientation (attitude) and heading of a vehicle or platform. AHRS combines measurements from accelerometers, gyroscopes, and often magnetometers through sensor fusion algorithms (typically Kalman filters or complementary filters) to provide a drift-free, fast attitude estimate. AHRS is standard in aviation, marine navigation, and modern autonomous systems.	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.