Maybe I am misunderstanding what you just wrote, but if you assume the the path will not overlap itself, then you won't have the problem you are trying to solve here anyway!? Don't those summits and loops in those parallel curves of the trajectory arise exactly from an overlapping path?
Another algorithm just comes to my mind, but it sure is not very efficient and probably very slow. First build you green and red paths. Then go along your trajectory and for every point in the trajectory set the coordinates for all points in both paths, which are within a distance of R from the point on trajectory, to NaN. Later use filterNaN() to delete those array elements. Its sort of letting Mathcad play milling machine.
To increase accuracy of the result you may additionally add points on the circumfence of the circle for those line segments where one point is inside and the other outside of the circle.