The real problem you have is one of reference frame. The curve it self is not important as it represents some path on the playing field frame of reference. The incremental control of the robot is based on its frame of reference to the center of the robot for example.
This is a common problem for aircraft, satellites and just about any navigation problem.
The solution is to use a series of translations and rotations. The best way to do that is with quaternions as they do the rotation without ambiquity.
http://en.wikipedia.org/wiki/Quatern...atial_rotation
has a good primer on the subject. This is commonly used for computer graphics and simulations.
Have fun