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Remove trailing spaces
The commands find . -type f -name '*.md' -exec sed --in-place 's/[[:space:]]\+$//' {} \+ and find . -type f -name '*.tex' -exec sed --in-place 's/[[:space:]]\+$//' {} \+ were used to do so.
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\chapter*{Introduction}
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When you want to develop a selfdriving car, you have to plan which path
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When you want to develop a selfdriving car, you have to plan which path
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it should take. A reasonable choice for the representation of
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paths are cubic splines. You also have to be able to calculate
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how to steer to get or to remain on a path. A way to do this
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is by applying the \href{https://en.wikipedia.org/wiki/PID_algorithm}{PID algorithm}.
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This algorithm needs to know the signed current error. So you need to
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This algorithm needs to know the signed current error. So you need to
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be able to get the minimal distance of a point (the position of the car)
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to a cubic spline (the prefered path)
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combined with sign (which represents the steering direction).
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@ -12,7 +12,7 @@ As one steering direction might be prefered, it is not only necessary to
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get the minimal absolute distance, but might also help to get all points
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on the spline with minimal distance.
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In this paper, I want to discuss how to find all points on a cubic
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In this paper, I want to discuss how to find all points on a cubic
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function with minimal distance to a given point.
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As other representations of paths might be easier to understand and
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to implement, I will also cover the problem of finding the minimal
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