This is a little demo I whipped up to answer this question in the Q&A section of the Godot Engine site.
Short description: the player is moved around by the left and right arrows. As the player moves near the flying chicken, it starts to pursue him. Under the hood, a number of Vector2Ds are created. These are combined with a Curve2D and this is used to move the chicken towards the player. While the code isn't perfect, it demonstrates the idea.
Screenshot
