collision detection – How can I find the closest point between an oriented bounding box and a capsule?

My capsule is defined by a center position with a radius and length. I have capsule/capsule, sphere/sphere, sphere/capsule, sphere/obb, obb/obb, and sphere/triangle collision working, but I cannot figure out how to do capsule/obb.

I know how to find the closest point on an obb to another point, the closest point on a line to another point, and the closest point between two lines.