Pure pursuit algorithm - Transform Global to vehicle coordinates?

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project: autonomous driving car

I have a small RC car, a Raspberry Pi and a camera which are fixed on the car. Now I want to let the car drive autonomous with image processing. So far I can detect the lane and get the point (x and y of the path on the image)

Now I want to implement the simple pure pursuit algorithm. While I was trying to understand the pure pursuit algorithm which is explained in this paper I read about "global and local coordinate system".

My question: Do I have to transform the (x,y) points of the path from the image to the vehicles coordinate system? If yes, how can I do this?