Consider a sphere with a point $A$ and point $B$ on it. In addition there are $k$ points on that sphere we call forbidden points. I am looking for a curve on that sphere from $A$ to $B$ that does not intersect with neighborhoods (loseley speaking circles) of the $k$ points.
The curve I am looking for should be at least differentiable and somehow "optimal", e.g. the shortest possible one.
Can anyone give me hints or refer to related literature?
I am dealing with an optimal control problem and found an Ansatz to solve it and now i would like to try another Ansatz.