Compute vector that points inside of a curve

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I am implementing a trajectory tracking algorithm, and I am having trouble computing the angle the robot should follow when there is a change in curvature. I think that using the vector that points inside the curvature could be really useful, but I do not know how to computer this vector.

Basically I need to compute the blue vector of this animation. Any ideas how I can compute this vector when I know the parametric equations of the curve.