Coordinate transformation from Cartesian to Frenet Frame
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Can anyone tell me how to convert from Cartesian to Frenet Frame for a vehicle driving on a curved road? In other words how do I convert from (x,y) -> (s,d) where is along the curve and d is perpendicular to the curve?
Is there a Matlab code someone can share?
For example if the vehicle is 1 m off centerline and driving along the arc of a circle at speed 1 m/s, then the coordinates at every 1 sec in Cartesian and Frenet frame are given by:
x = cos(theta) ... [with the appropriate scalings for radius and speed]
y = sin(theta) ... [with the appropriate scalings for radius and speed]
s = (0, 1, 2, ...)
d = (1, 1, 1, ...)
I have been looking into Matlab codes but the solutions I got are in the form of (T, N, B) - the tangent, normal and binormal. How do I convert them to distance along the centerline and perpendicular to the centerline?