Coordinate transformation from Cartesian to Frenet Frame
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Suvo Ganguli 2021 年 3 月 9 日
回答済み: Cameron Stabile 2023 年 1 月 26 日
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?
M I 2021 年 5 月 21 日
i recently found this: https://github.com/fjp/frenet/blob/master/matlab/Cart2FRT.m
回答 (1 件)
Cameron Stabile 2023 年 1 月 26 日
The referencePathFrenet feature from the Navigation Toolbox might be of use to you. The feature fits a piece-wise clothoid spline between a set of or waypoints, after which you can convert between Cartesian and Frenet space.
There are a number of tools at your disposal, which loosely fall into the following categories:
Projection XY point to Curve:
- closestPoint - Find closest point on reference path to global point
- closestProjections - Find orthogonal projections between path tangent vector and query point
- closestPointsToSequence - Projects sequence of points onto path
Conversion between Cartesian and Frenet
- frenet2global - Convert Frenet states to global states
- global2frenet - Convert global states to Frenet states
Evaluating Curve at Arclength (S)
- interpolate - Interpolate reference path at provided arc lengths
- position - Return xy-position at arclength
- tangentAngle - Return tangent angle at arclength
- curvature - Return curvature at arclength
- changeInCurvature - Return change-in-curvature at arclength
There are also a number of examples that show how this can be applied to road-based planners, a good one to get you started could be Highway Trajectory Planning Using Frenet Reference Path.
Hope this helps,
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