#Frenet

Articles: 3

1. Frenet Arc-Length Conversion

   An interactive examination of how closely the oriented arc-length increment of a vehicle trajectory matches the reference-path arc-length increment under different vehicle states.

2. Frenet Vehicle Kinematics

   Defines the vehicle's Frenet state through the closest-point projection of the rear-axle center, derives a three-state time-domain model and a two-state reference-path-arc-length-domain model under the no-sideslip kinematic assumption, and explains arc-length conversion, the coordinate validity domain, and sign conventions for reversing.

3. Planar Frenet Frame

   Defines the unit tangent, left unit normal, and signed curvature of a planar reference path; derives the Frenet differential relations from both the orthonormal-frame and path-heading representations; and establishes consistent geometric and sign conventions for vehicle kinematics in Frenet coordinates.